Laminated acoustic window



Nov. 15, 1960 E. M. MCMILLAN 2,960,175

LAMINATED ACOUSTIC WINDOW i Filed June 6, 1946 3 Sheets-Sheet 1 FIG. I FIG. 2

INVENTOR.

EDWIN M. MGM l LLAN Attorney 1960 E. M. MCMILLAN 2,960,175

LAMINATED ACOUSTIC WINDOW Filed June 6, 1946 3 Sheets-Sheet 2 PEG. 5

AP AP INVENTOR.

EDWIN M. McMlLLAN Attorney Nov. 15, 1960 E. M. M MILLAN 2,960,175

LAMINATED ACOUSTIC WINDOW Filed June 6, 1946 5 Sheets-Sheet 3 W souuo l;

K GENERATOR uoulo MEDIUM INVENTOR.

EDWIN M. McMlLLAN 2,960,175 Egg Patented Nov. 15, 1960 LAMINATED ACOUSTIC WINDOW Edwin M. *McMillan, Berkeley, Galifi, assignor to the United States of America as represented by the Secretary of the Navy Filed June 6, 1946, Ser. No. 674,901

3 Claims. c1. 1s1-.s

My invention relates to systems for transmitting sound waves through a plurality of fiat plates.

It has been the practice in this art to use a single plate, a half-wave length thick, to obtain a phase difference of 180 between the entering and leaving faces, thus making the half-wave plate transparent to sound waves. My invention uses two flat plates of very small thickness to effect high transmission of the sound wave. It has less weight, is less critical as to frequency than the singleplate window, and has advantages in structure that might otherwise have to use half-wave plates.

In accordance with my invention, a plurality of flat plates are so dimensioned and arranged as to secure markedly high transmission of sound waves over a wide angular range.

Further in accordance with my invention, by using the multiple-layer principle a wall can be constructed which is highly transparent to high frequency sound and also thick enough to have considerable strength.

My invention further resides in systems having features hereinafter described and claimed.

For an understanding of my invention and for illustration of examples thereof, reference is made to the accompanying drawings, in which:

Fig. l is a sketch of a single incident ray hitting a plate.

Fig. 2 is a sketch of a plane wave with its composite rays hitting a plate.

Fig. 3 is a sketch of a wave hitting a single boundary.

Fig. 4 is a diagram of a sound wave being transmitted through a plate, showing the incident and reflection angles.

Fig. 5 is a diagram of a two layer plate, showing incoming plane wave being transmitted through both plates.

Fig. 6 is a diagram of a sound wave being transmitted through two plates of width d, spaced a distance h apart.

Fig. 7 is a section through a diagrammatically illustrated sound generator housing provided with a laminated window formed in accordance with the principles of the invention.

Figs. 1, 2, 3 are illustrative of the physical principles embodied in my invention. In Fig. 1, a single incident ray 1 gives rise to innumerable reflected and transmitted rays 2, because of the multiple reflections within a flat plate 3 such as steel.

In Fig. 2, rays 4, 5, 6 are parts of a plane Wave. Ray 4 takes the most direct path through the plate 8 to the composite transmitted ray 7. Ray 5 reaches the plate earlier than 4 but its contribution makes three trips across the plate before emerging as part of ray 7, and so may have either an earlier or later phase than the contribution from ray 4. Similarly the contributions from ray 6 will differ from 5 in the same way. There are several discrete pathlengths across the plate that make all these contributinuatio'n 6f'4, if a phase shift is" assigned toth'e passage r 2 tions have the same phase when they emerge as parts of the outgoing ray 7. (Path length depends on both plate thickness and angle of incidence.) For other path lengths the several contributions to ray 7 will have different phases, and so the phase of 7 varies with this path length. Thus the ray 7 may be thought of as being simply a conthrough the plate.

In Fig. 3, a wave 11 impinging upon a single boundary 9 divides into a reflected wave 12 and a transmitted wave 10. The reflected wave has a phase change relative to the incident wave, and the transmitted wave is in phase with the incident wave. No other phase values are pos-' sible.

The problem of the transmission of sound at normal incidence through a flat plate, or any parallel combination of flat plates, is easily solved by standard methods. The same problem for the case of oblique incidence is not easily solved and is of importance, for example, in the design of streamlined housings for underwater sound projectors. In this note two cases are considered: (1) A single flat plate, with the same medium on both sides; (2) Two parallel flat plates, with the same medium between them as well as on both outer sides. In each case the transmission of an unbounded plane wave is computed, under the assumption that the material of the plate acts like a fluid as far as the transmission of sound is concerned.

In deriving the following formulas, the rigidity of the plates has been neglected. This leads to some error in the case of oblique incidence, but not for normal incidence.

NOTATION where f=frequency, c=velocity of sound, t=wavelength.

p=density. =angle between ray and normal to plate.

The above quantities without primes refer to the medium outside the plates, with primes to the material of the plates.

d=thickness of plates.

h=distance between plates (in case II).

A =transmitted pressure amplitude for unit incident amplitude.

A =reflected pressure amplitude for unit incident amplitude.

T=fractional transmission of energy.

e =phase shift in transmitted wave.

R=fractional reflection of energy.

e =phase shift in reflected wave (computed as if the reflection took plate at the surface of first incidence).

The following abbreviations will be used:

The relation between on and a is given by Snells law:

k sin a=k' sin a Case I ItI we v assume now that k and k are real (non-dissipatiyejjmedia), the separation into intensity and phasecan be'carried'out, and:

Referring to Fig. 4, if k is less than k, there willbe acriticalf angle of incidence (or) at which 0: becomes a right angle,'and at which total reflection will occur in the case of reflection from a boundary. In the case of the plate there will be a finite amount of transmission beyond this angle.

given by Snells law is greater than 1, and:

cos a'== /1sin a=jx sin (JR-1f Then -Q=.-]'lQl, cos 0=cos hi0! sin 0'=j sin hlfi'f :(3) Thus all the results of this section remain valid for angles beyond the critical angle, if the following substitutions are made:

At the critical angle (3) and (10) approach the limiting form:

1 1 z I 1+ 1Q| 1 m +%(%ki cos a) The form (11) is also a useful approximation to both Beyond the critical angle, .sin .a' as 4 (3) and (10) for all cases in which 0 1, Q l; for example, it gives nearly correct results up to 0c=45 for steel plates of thickness small compared to a quarter wavelength, immersed in water.

Case II In Fig. 5 are two parallel plates or groups of plates, with amplitude transmission and reflection coeflicients B B and C C respectively, and spaced a distance h apart. Then the transmission of a wave through the combination can be computed by considering the multiple reflections between the two, and combining the many transmitted fractions with the proper phases. The phase difierence between two successive transmitted waves =2kh cos a=2 Then:

AT=BTcTu+BRcBexpe2js+ RcR exp =41 0+ .1

2 4%] AR 'BR+BT CRGZZKV (13) (Note that in case either or both of the reflectors is an unsymmetrical group of plates, the Bs and Cs may be different for the two directions of incidence, and the values for the appropriate directions, as determined by tracing the rays in' the figure, must be used.)

This method canbeused to find the transmission and reflection coeflicients of any combination of plates, by starting with two, getting the Bs and Cs'from part I, then using the resulting coefiicients for the pair to combine with the next one, and so on. In Fig. 6 is repre. sented the simple case of two equal plates, each of thickness d, with-no dissipation in the plates or in the medium. The computation for the transmission coefficient only is carried out.

-From equations 3 6.

BTCT=.

The denominator of. this expression can be interpreted as. the sum of two vectors, of lengths ees with the angle -2( I'+) between them. Thus it takes all values between 1 and i i as h (and therefore 5) is varied. The separation into intens ty and phase is now easily done, with the result:

and v 5 a o-n is obtained by substituting I ied cos a) in (17) and (l8),and for (Q tan 6 in the definition of I.

The closest spacing of the plates for complete transmission is given by the condition for This can be put into the form:

kcosa In the limiting case mentioned in the preceding paragraph, this becomes:

I sinl: ied cos 11/] cos a DISCUSSION OF RESULTS, WII H SOME NUMERICAL VALUES We are particularly interested in the case of steel plates immersed in sea water. For this case,

k/k'=3.31 p'/p=7.85 k:0.l09 f inches* with f in kilocycles With these values we can make the following table:

TABLE 1 4! cos a [cos a'[ ]Q,|

The critical angle is 17 35'.

The approximate form (11) is seen to be applicable, with errors of a few percent, up to an angle of incidence of 45 and a thickness of for f==70 kc., or correspondingly greater thicknesses for lower frequencies.

TRANSMISSION THROUGH A SINGLE THIN PLATE Some values of T and e for a single thin plate are given in Table 2, for various values of kd, where kd=0.109 f (kilocycles) d (inches) TABLE 2 Note that values of 'I trorn the formula are multiplied by 100] ltd a T(Per --r cent) (degrees) For f==70 kc. and d= kd=0.477, so that the energy transmission at normal incidence is less than 25%, which seems too small if the plate is to be part of a streamlined shell over a projector. To get 75% transmission at normal incidence for 70 kc. the plate would have to be about 0.02" thick.

TRANSMISSION THROUGH A SINGLE THICK PLATE For angles of incidence greater than the critical angle, the transmission decreases indefinitely as the plate is made thicker, but for angles of incidence less than the critical angle, T is a periodic function of d. In this case. T has a minimum value of at the thickness where then returns to complete transmission at and so on. (In other words, complete transmission occurs if d cose a is an integral multiple of a half wave-length of the sound in steel.) This suggests that a half-wave plate would be a good material for a streamlined cover, but the large value of Q makes the condition for transmission very critical, as seen from the form of Equation 3. For example, if the thickness is made just a half wavelength, to give complete transmission at normal incidence, only 25% transmission will occur at a 5 angle of incidence. This is too critical for most uses. Such a plate might find some application as a sort of directional filter.

TRANSMISSION THROUGH A PAIR OF THIN PLATES The above paragraphs make it seem difficult to construct a wall that will be highly transparent to 70 kc. sound, and will also be thick enough to have considerable strength, but the use of a double-layer wall offers a possible way of accomplishing this. Equation 17 shows that complete transmission through a double layer is obtained for certain values of the spacing between layers. To find the angular dependence of the transmission for fixed dimensions of the layer, we shall have to make some numerical computations.

We have computed the case of 70 kc. sound trans 7 mitted through two sheets of steel (kd=0.477). We :have 'two values of the spacing; first, 0.064 inch (kh=0.492), giving .complete transmission at normal incidenceyand second, 0.072 inch (kh=551), giving complete transmission at 20 angle of incidence. The results are given in Table "3.

" TABLE 3 n=.0a4" n=.o72"

. a T (Per- -eT '1 (Per- -e'r cent) (degrees) cent) (degrees) These results show'that good transmission of kc. sound canbe obtained overv a wide angular range, through a layer having considerable mechanical strength, by using the double layer principle.

Whatis claimed is:

--1.'In a-liquid medium sound transmission system for frequencies of the order'of seventy kilocycles per second,

asound pressure generator and a housing therefor, a laminated window in said housing comprising a plurality of metallic plates arranged insubstantially parallel'spaced relationship along an axis substantially normal to a surface of said housing, each plate having a thicknessof. the order of one sixteenth of an inch, the spacing between *saidplates-being of the order of 0.060 to 0.075 inch and a liquid medium 'inside'and outside saidhousing and filling T the-spaces :be'tween's'aidplates whereby a high ,percentage of sound transmission through said window is obtained over a wide range of incident angles of sound waves on said window.

2. lniafiuid medium s'ound transmission system having a soiind pressure generator and a housing therefor, a

References Cited in the file of this patent UNITED STATES PATENTS 1,117,766 Berger Nov. 17, 1914 1,440,361 Hopwood Dec. 26, 1922 1,450,287 Hahnemann Apr. 3, 1923 '-1,"451,422. .Hahnemann Apr. 10, 1923 1,563,626 Hecht et a1. Dec. 1, 1925 2,423,459 Mason July 8, 1947 Peterson Oct. 26, 1948 

